Most Facebook page administrators manage their pages from behind a regular Facebook account. That means that they can see the same information about you that other Facebook users see. How much they can see depends on what you allow the following groups to see: Friends, Friends of Friends, Networks and Everyone.
Facebook allows you to customize your profile info to show or not show to these groups. As I've mentioned before, you can further break this down to hide info and activity from certain groups of people. To do this, click Account>Privacy Settings>Custom>Customize Settings.
While you're at it, go ahead and customize the information that appears when users search for your name.
Click Privacy Settings>View Settings and change the dropdown on each profile section that will show when a user looks you up in a search, depending on the category they fall in. Since I belong to fairly wide networks, I limit visibility of detailed information such as my friend list, hometown and activities to Friends Only. Since I want people outside of my Friends and Networks to be able to find me, I allow Everyone to search for me and send me direct messages and friend requests. People I have connections with may have an easier time recognizing me if they are able to see my education and work info, so I share that with Networks and Friends.
Customizing your privacy settings, especially since they usually default to "Everyone", will ensure that Facebook page administrators can only see the information you are willing to share with the general public.